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Perpetuity (Capitalized Perpetuity (Capitalized Cost)Cost)

Perpetuity (Capitalized Perpetuity (Capitalized Cost)Cost)• Occasionally, donors sponsor Occasionally, donors sponsor

perpetual awards or programs perpetual awards or programs by a lump sum of money earning by a lump sum of money earning interest.interest.

• The interest earned each period The interest earned each period (A) equals the funds necessary (A) equals the funds necessary to pay for the ongoing award or to pay for the ongoing award or program.program.

The relationship is A = P( i ) The relationship is A = P( i )

• This concept is also called This concept is also called capitalized costcapitalized cost (where CC = P). (where CC = P).

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Perpetuity ExamplePerpetuity ExamplePerpetuity ExamplePerpetuity ExampleA donor has decided to establish a $10,000 per year scholarship. The first scholarship will be paid 5 years from today and will continue at the same time every year forever. The fund for the scholarship will be established in 8 equal payments every 6 months starting 6 months from now.

Determine the amount of each of the equal initiating payments, if funds can earn interest at the rate of 6% per year with semi-annual compounding.

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Perpetuity ProblemPerpetuity ProblemPerpetuity ProblemPerpetuity ProblemGiven:Given:

A = 10 000 per year, every year after Year 5A = 10 000 per year, every year after Year 5n = 8 payments @ 6 mo. intervals, starting @ 6 n = 8 payments @ 6 mo. intervals, starting @ 6

mo.mo.i = 6%, cpd semi-annually i = 6%, cpd semi-annually

Find Amount of Initiating payments Find Amount of Initiating payments (A(Ai i ):):

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Complex Flows and Complex Flows and PerpetuityPerpetuity

Complex Flows and Complex Flows and PerpetuityPerpetuityIn some circumstances, there is a mix In some circumstances, there is a mix

of recurring and non-recurring or one-of recurring and non-recurring or one-time cash flows that must be time cash flows that must be capitalized for perpetuity.capitalized for perpetuity.

These mixed flows may be accounted These mixed flows may be accounted for by:for by:

1.) finding the 1.) finding the NPWNPW of all the of all the one-one-timetime and and non-recurringnon-recurring cash cash flows (flows (= CC= CCPart 1Part 1 ))

2.) finding the 2.) finding the Annual EquivalentAnnual Equivalent of of one cycleone cycle of all the of all the recurringrecurring cash flows, and then computing P cash flows, and then computing P ((= CC= CCPart 2Part 2) from the perpetuity ) from the perpetuity relationship A = P(i)relationship A = P(i)

3.) summing (1.) and (2.) to find the 3.) summing (1.) and (2.) to find the total capitalized cost: total capitalized cost:

CCCCTotalTotal = CC = CCPart 1Part 1 + CC + CCPart 2Part 2

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Capitalized Cost ExampleCapitalized Cost ExampleCapitalized Cost ExampleCapitalized Cost Example

The SD School of Minds wants to build The SD School of Minds wants to build a soccer stadium. It will cost $ 5 000 a soccer stadium. It will cost $ 5 000 000 to construct, and $ 7 000 each 000 to construct, and $ 7 000 each year to clean. In 20 years, the year to clean. In 20 years, the contractor will return to tighten all the contractor will return to tighten all the bolts on the stadium structure, and bolts on the stadium structure, and they will charge $ 90 000 (one time they will charge $ 90 000 (one time cost). cost).

Every 15 years, they will replace the Every 15 years, they will replace the artificial turf at a cost of $ 50 000. artificial turf at a cost of $ 50 000. Plant services will pay $ 80 000 each Plant services will pay $ 80 000 each year to mow and water the artificial year to mow and water the artificial turf. turf.

At a 4% annual cost of capital, how At a 4% annual cost of capital, how much should they ask of the donors, much should they ask of the donors, for the honor of putting their name on for the honor of putting their name on the stadium?the stadium?

Class Problem

Calculate the capitalized cost of a project that has an initial cost of $150,000 and an additional investment cost of $50,000 after 10 years. The annual operating cost will be $5000 for the first 4 years and $8000 thereafter. In addition, there is expected to be a recurring major rework cost of $15,000 every 13 years. Assume that i= 15%/ year.

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